3d6
3d6 denotes rolling three six-sided dice and summing the results. Each die is fair, with faces numbered 1 through 6, and the three dice are rolled independently. The notation is common in tabletop role-playing games and probability exercises. The sum ranges from 3 to 18. The distribution is the convolution of three uniform dice, producing a symmetric, unimodal curve with the highest probability at totals of 10 and 11. Specifically, 10 and 11 each occur in 27 of the 216 possible outcomes (about 12.5%). The next most likely totals are 9 and 12 (25/216 ≈ 11.6%), followed by 8 and 13 (21/216 ≈ 9.7%), and so on down to 3 and 18 (1/216 ≈ 0.46%). The mean is 10.5 and the standard deviation is approximately 2.96.
Probability for a given sum s is the number of ordered triples (a,b,c) with a,b,c in {1,...,6}
In use, 3d6 appears in various games and simulations for tasks such as attribute generation or skill